Problem: Simplify the following expression: $n = \dfrac{t^2 - 4t - 5}{t - 5} $
Answer: First factor the polynomial in the numerator. $ t^2 - 4t - 5 = (t - 5)(t + 1) $ So we can rewrite the expression as: $n = \dfrac{(t - 5)(t + 1)}{t - 5} $ We can divide the numerator and denominator by $(t - 5)$ on condition that $t \neq 5$ Therefore $n = t + 1; t \neq 5$